The planar compound eye imaging system uses multiple sub-apertures to image the scene. With a proper optical design, the planar compound eye has the characteristics of thin, light, and large field of view. However, because of the constraint of imaging sub-aperture size and spatial sampling rate of the image sensor, the image quality of each sub-aperture is low. How to fuse multiple sub-aperture images to obtain a high-resolution image is an urgent problem. Multi-image super-resolution theory uses multiple images with complementary information to reconstruct high spatial resolution images. However, existing theories usually use oversimplified motion models, and this motion model is not suitable for planar compound eye imaging. If the existing multi-image super-resolution theory is directly applied to the resolution enhancement of planar compound eye, the inaccurate relative motion estimation will reduce the performance of image resolution enhancement. In order to solve these problems, the motion model of the multi-image super-resolution is improved in the variational Bayesian framework, and the derived joint estimation algorithm is used to enhance the resolution of the planar compound eye. In the first stage of hierarchical Bayesian model, we use total variation (TV) model and non-informative prior model to model the latent high-resolution image and the motion vector, respectively. In the second stage, we use Gamma distribution to model the model parameters in the first stage. Instead of the oversimplified Euclidean motion model, we use the affine motion model, which is more suitable for planar compound eye imaging scenario. The correctness and effectiveness of the proposed method is verified by the simulation data experiments and the real compound eye data experiments. We report the experiments and analyses on simulated and real data. For the experiments on simulated data, the performance of the resolution enhancement method is quantitatively measured by the peak signal-to-noise ratio (PSNR). The proposed method is superior to the comparison methods in all simulated scenarios, especially in the middle and high signal to noise ratio scenarios. Better visual effects of the results also demonstrate the advantage of the proposed method. For the real data experiments, we first e USAF 1951 and ISO 12233 resolution charts as the target at a certain distance, and use the planar compound eye prototype to collect the compound eye images. Then, the resolution chart compound eye images are used to compare different resolution enhancement methods. The proposed method has better performance in preserving image details, suppressing noise and removing artifacts.